Performance of currency portfolios chosen by a Bayesian technique: 1967–1985

Abstract

This paper is about normative currency portfolio rules. It assumes logarithmic investors who maximize the expected utility from lognormal currency returns with and without short sales restrictions. A number of implementable portfolio diversification policies are tried out on a large body of data covering nine major currencies and eighteen years of weekly observations. In doing so, we present ways of dealing with the ‘estimation risk’ in an international context. The necessary mean and covariance inputs are provided by a Bayesian prior on the means and by sample means and covariance matrices, which are estimated from weekly sample data. While some policies do produce abnormal returns (over and beyond proper reward for risk), none does so in a statistically significant way. This means that the evidence does not allow one to conclude that market participants are improperly diversified. As a byproduct of this investigation, techniques are found which would allow portfolio managers to earn a proper reward for risk by following a purely mechanical procedure; such techniques may be valuable in a multi-country world where the aggregate portfolio of currencies and securities is unknown and is not supposed to be efficient.